STUDIES IN ASTRONOMICAL TIME SERIES ANALYSIS. VI. BAYESIAN BLOCK REPRESENTATIONS

By J. Scargle, Jay Norris, B. Jackson, J. Chiang. 2012

341 citations recorded by the source corpus.

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it—an improved and generalized version of Bayesian Blocks—that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multivariate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by Arias-Castro et al. In the spirit of Reproducible Research all of the code and data necessary to reproduce all of the figures in this paper are included as supplementary material.

Subfields: Artificial Intelligence, Statistics and Probability, Signal Processing

View Paper: https://www.semanticscholar.org/paper/30a6830e9f12003437d5610cafe05e1ee525e9ca

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

In Signal Processing

Citations in the corpus

2FHL: THE SECOND CATALOG OF HARD FERMI-LAT SOURCES (2015, methodology): “This algorithm, designed to detect and characterize variability in time series (Scargle 1998; Scargle et al. 2013), is well suited in regimes of low-count statistics.”
Inferring spatial and signaling relationships between cells from single cell transcriptomic data (2020, methodology): “35).”
IDEPI: Rapid Prediction of HIV-1 Antibody Epitopes and Other Phenotypic Features from Sequence Data Using a Flexible Machine Learning Platform (2014, methodology): “…structure to perform a spatial neighborhood analysis, and an adaptive discretization algorithm for continuous features (e.g. using Bayesian blocks [66]), required by mRMR. Downstream users that build novel feature extractors are recommended to submit their creations to IDEPI, via GitHub’s pull…”
THE FIRST FERMI-LAT GAMMA-RAY BURST CATALOG (2013, methodology): “We tested several binning schemes, including linear, logarithmic, and Bayesian-blocks binning, and the resulting likelihood fit parameters were consistent among the different choices.”
THE FIRST FERMI-LAT CATALOG OF SOURCES ABOVE 10 GeV (2013, methodology): “For the analysis of the 1FHL data, the fitness function used is the logarithm of the maximum likelihood for each individual block under the constant local rate hypothesis, as described by Scargle et al. (2013).”
Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures (2016, methodology): “A more sophisticated approach is the Bayesian blocks algo-rithm (Scargle et al. 2013), in which the number and widths of bins are chosen by optimising a fitness function, without constraining the bins to be of equal width.”
An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A (2017, methodology): “Initially, the TTE data for NaI detectors 1,2 and 5 were investigated ±5 seconds on either side of the GBM trigger time of GRB 170817A and analyzed using a false positive probability (p0) of 0.05, previously determined to be a good value from studies by Scargle et al. (2013).”
3FHL: The Third Catalog of Hard Fermi-LAT Sources (2017, methodology): “In particular, this analysis can be applied to lowcount data (Scargle 1998; Scargle et al. 2013).”